Approximating Spanning Trees with Low Crossing Number
نویسنده
چکیده
We present a linear programming based algorithm for computing a spanning tree T of a set P of n points in IR, such that its crossing number is O(min(t log n, n1−1/d)), where t the minimum crossing number of any spanning tree of P . This is the first guaranteed approximation algorithm for this problem. We provide a similar approximation algorithm for the more general settings of building a spanning tree for a set system with bounded VC dimension. Our approach is an alternative to the reweighting technique previously used in computing such spanning trees.
منابع مشابه
Low-Crossing Spanning Trees - An Alternative Proof and Experiments
We give a quick proof that any planar n-point set has a spanning tree with crossing number O( √ n). Our proof relies on an LP-based approach by HarPeled [8], and it uses Farkas’ lemma. We also present a new heuristic for computing a spanning tree with low crossing number and compare it experimentally with other known approaches.
متن کاملOn relation between the Kirchhoff index and number of spanning trees of graph
Let $G=(V,E)$, $V={1,2,ldots,n}$, $E={e_1,e_2,ldots,e_m}$,be a simple connected graph, with sequence of vertex degrees$Delta =d_1geq d_2geqcdotsgeq d_n=delta >0$ and Laplacian eigenvalues$mu_1geq mu_2geqcdotsgeqmu_{n-1}>mu_n=0$. Denote by $Kf(G)=nsum_{i=1}^{n-1}frac{1}{mu_i}$ and $t=t(G)=frac 1n prod_{i=1}^{n-1} mu_i$ the Kirchhoff index and number of spanning tree...
متن کاملOptimal Self-healing of Smart Distribution Grids Based on Spanning Trees to Improve System Reliability
In this paper, a self-healing approach for smart distribution network is presented based on Graph theory and cut sets. In the proposed Graph theory based approach, the upstream grid and all the existing microgrids are modeled as a common node after fault occurrence. Thereafter, the maneuvering lines which are in the cut sets are selected as the recovery path for alternatives networks by making ...
متن کاملCounting the number of spanning trees of graphs
A spanning tree of graph G is a spanning subgraph of G that is a tree. In this paper, we focus our attention on (n,m) graphs, where m = n, n + 1, n + 2, n+3 and n + 4. We also determine some coefficients of the Laplacian characteristic polynomial of fullerene graphs.
متن کاملLower bounds on the maximum number of non-crossing acyclic graphs
This paper is a contribution to the problem of counting geometric graphs on point sets. More concretely, we look at the maximum numbers of non-crossing spanning trees and forests. We show that the so-called double chain point configuration of N points has Ω(12.52 ) noncrossing spanning trees and Ω(13.61 ) non-crossing forests. This improves the previous lower bounds on the maximum number of non...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/0907.1131 شماره
صفحات -
تاریخ انتشار 2009